Exotic Decays of a Vector-like top Partner at the LHC

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UPTEC F 19038

Examensarbete 30 hp September 2019

Exotic Decays of a Vector-like top Partner at the LHC

Alexander Skwarcan-Bidakowski

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Teknisk- naturvetenskaplig fakultet UTH-enheten

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Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

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018 – 471 30 03

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Abstract

Exotic Decays of a Vector-liketop Partner at the LHC

Alexander Skwarcan-Bidakowski

An evaluation of how sensitive some ATLAS searches for new physics are to a new beyond standard model (BSM) vector-like quark (VLQ) and a pseudo Nambu-Goldstone boson (pNGB) scalar. This was done by simulating a signal containing these new particles and making a recast of it onto existing verified ATLAS searches for new physics at center-of-mass (CM) energy of 13 TeV (Run 2) at the Large Hadron Collider (LHC). Signals for recasting were tailored such that their final states would be appropriate in relation to each respective ATLAS search in order to use the same selection criteria as applied in the existing searches. The results are summarized in the form of significances (Z) for each masspoint of the new top-partner and S particle. Significances did not show any expectiation of excluding any masspoint in the examined mass range for the recasts at 95% CL.

This suggests that a dedicated search for these particles in the considered masspoints would be required.

ISSN: 1401-5757, UPTEC F 19038 Examinator: Tomas Nyberg

Ämnesgranskare: Elin Bergeås Kuutmann Handledare: Venugopal Ellajosyula

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Populärvetenskaplig sammanfattning

Forskning inom partikelfysik är mänsklighetens strävan till att kunna svara på frågorna: Vad är universums minsta beståndsdelar? Hur växelverkar dessa beståndsdelar med varandra för att skapa allt runt oss? Dessa beståndsdelar, sk. elementarpartiklar, med dess fyra fundamentala naturkrafter; svag-, stark växelverkan, elektromagnetism och gravitation är vad som får vårt uni- versum att se ut som det gör. Det som vi vet om universumet beskrivs av teorin av den sk.

Standardmodellen som har varit väldigt framgångsrik, speciellt efter att den sista pusselbiten - Higgsbosonen hittades år 2012 i partikelacceleratoranläggningen Large Hadron Collider (LHC) av ATLAS och CMS experimenten. Upptäckten av Higgsbosonen bekräftade Higgsmekanismen som beskriver hur elementarpartiklarna får sin massa.

Standardmodellen har dock fortfarande vissa problem. Ett av dem är den enorma skillnaden mellan den teoretiskt beräknade och den upptäckta massan av Higgsbosonen. Enligt teorin ska Higgsbosonens massa ha kvantkorrektioner som divergerar med storleksordningen 10¹⁹ GeV, men observationerna har uppmätt massan till att vara ungefär 125 GeV. Detta tyder på att det kan finnas en sorts finjustering av kvantkorrektionerna som resulterar i den lägre uppmätta massan.

Probemet kallas för finjusteringsproblemet och leder till teorier bortom Standardmodellen som ska lösa problemet. En av många teorier är den sammansatta Higgsmodellen som förutspår en ny partikel kallad för toppartnern som är en tung vektorlik kvark lik den toppkvark som beskrivs i Standardmodellen. Tidigare analyser och sökningar har enbart tittat på toppartnerns söderfall till Standardmodellpartiklarna W b, Ht, Zt.

Detta examensarbete studerar sönderfallet av toppartnern till en ny exotisk skalär partikel, S och toppkvarken. Partikeln anses vara elektriskt neutral i laddning och antas sönderfalla till Standardmodellpartiklarna, S → W W , S → ZZ och S → Zγ. Studien går ut på att simulera proton-protonkollisioner som skapar toppartnern och dess söderfallsprodukt S, vars signal sedan omarbetas på existerande analyser för att se om dess paramenterutrymmen redan varit exkluderat av dem. Syftet med denna studie är att ge både teoretiker och experimentalister en uppskattning om vilka massor dessa två nya partiklar kan ha. Detta ska förhoppningsvis leda till en dedikerad analys och sökning efter toppartnern och S-partikeln i de givna sönderfallskanalerna.

Studien visade att inga signaler med de utvärderade massorna av toppartnern och S-partikeln skulle kunna exkluderas av de existerande analyserna, vilket tyder på att modellen har potential och bör undersökas vidare.

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1 Introduction

Through the ages, people have pondered the question of what the universe is made of. In the last century it was thought that the universe consists of the smallest particles - protons, neutrons and electrons, but in the advent of particle accelerators and detectors, the basic building blocks of our universe were demonstrated to be even smaller. The Standard Model of particle physics (SM), developed over the last few decades and used today, describes these elementary particles and the interactions between them. The interactions correspond to the four fundamental forces of nature - the Strong, Weak, Electromagnetic forces and gravity¹. In 2012, the discovery of the Higgs boson at the Large Hadron Collider (LHC) by the ATLAS [1] and CMS [2] collaborations was a great feat, validating the Higgs mechanism and completing the SM, for which the Nobel prize in physics was awarded in 2013. However, the SM cannot completely explain dark matter, neutrino masses, matter- antimatter asymmetry or gravity and was thus considered just a part of a more fundamental theory. When calculating the Higgs mass theoretically, the radiative corrections to the Higgs mass diverge in orders of the Planck scale² squared, Λ². This is a large discrepancy when comparing to the experimentally discovered Higgs boson with a mass of 125 GeV [1, 2].

An explanation to why the Higgs boson mass is so light is that there seems to exist some kind of delicate fine-tuning of the corrections. This is called the Hierarchy problem or more specifically the fine-tuning problem. These problems in the SM make it necessary to consider alternative models or extensions to it. There are many promising Beyond the Standard Model theories (BSM) which address the Hierarchy problem, one central to the thesis being the Composite Higgs Model (CHM).

In the CHM, the Higgs boson is considered to arise as a massive pseudo Nambu-Goldstone Boson (pNGB) through an approximate symmetry breaking³ of a SO(5) → SO(4) gauge group for the minimal CHM. Together with the pNGB Higgs, the CHM also predicts the existence of massive spin-1/2 vector-like quarks (VLQ). Previous searches for a hypothetical vector-like top particle, called the top-partner [3], have considered it decaying into electroweak bosons and 3rd generation quarks,

T → W b, T → Ht, T → Zt. (1.1)

However, this thesis considers the top-partner to decay into a new hypothetical particle [4], S⁴and a top quark,

T → St. (1.2)

The S particle is a charge neutral, massive scalar which couples to electroweak bosons and comes from an extended CHM.

In this thesis, existing analyses searching for new physics were used in attempt to constrain the parameter space⁵ of the extended Composite Higgs Model, with the method of recasting. Final states of the signals were tailored such that they would pass the selection criteria imposed by the searches, in order to obtain as many predicted signal events as possible in contrast to the background events calculated in the searches⁶. Using the predicted and background events, a sig-

1Gravity is, however, not included in the Standard Model because its effect is so weak its negligible.

2Where the Planck scale is Λ = 10¹⁹GeV

3Instead of an exact symmetry breaking, giving rise to massless NGBs, like the SM predicts.

4In some literature S is knows as η.

5Possible top-partner and S particle masses.

6Effectively reusing backgrounds generated in previous searches. More on that in Sec.(4).

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nificance could be calculated for each masspoint (combination of top-partner and S particle mass) in attempt to find a 95% CL expectation to exclude it. The thesis aims to provide a guideline for theorists and experimentalists to know which parameter spaces are expected to be excluded, such that their work can be focused in the right direction when confronting this model. Additionally, the thesis suggests a dedicated search for these particles in the masspoints suggested.

Appropriate signals based on the CHM are simulated using MadGraph 5 [5] and hadronized with Pythia8 [6]. A fast detector simulation is done through Delphes 3 [7] and finally, the signals are recast through CheckMate 2 [8] on verified Run 2 ATLAS analyses with a center-of-mass energy

√s = 13 TeV for proton-proton collisions. The thesis starts with an introduction to particle physics in Sec.(2), the mathematics of Quantum Field Theory (QFT) in Sec.(2.2) and the Higgs mechanism in Sec.(2.3). This is followed by a qualitative description of the minimal CHM in Sec.(2.5) and the considered model in Sec.(2.6). Finally, recasting is explained in Sec.(4) followed by the results and conclusion in Secs.(5) and (6).

2 Theory

The theoretical part of this paper will start with a recap of the Standard Model and the electroweak symmetry breaking induced by the Higgs mechanism followed by the Composite Higgs model. The particles of interest are presented together with their possible decay channels.

2.1 Standard Model of Particle Physics

The Greek philosopher Democritus suggested that there had to exist tiny, indivisible, solid objects that make up all the matter in the universe. He called these objects atoms, a word that was later used by the English chemist John Dalton to describe elements of the periodic table - objects he believed could not be divided, created or destroyed. Today we know, however, that atoms are combinations of protons, neutrons and electrons and can be divided through fission or changed into other atoms by altering the number of protons and neutrons in the nucleus. We also know that protons and neutrons are composite, meaning that they consist of even smaller objects we call elementary particles. These point-like particles are considered the most basic building blocks for all matter in the universe. The mechanism of interaction between the particles is through the four fundamental forces of nature: the strong force, the weak force, the electromagnetic force and gravity. The strong force holds nucleons and nuclei together, while the electromagnetic force keeps the electrons in orbit and combines atoms to form molecules. The weak force is the mechanism between subatomic particles responsible for radioactive decay. Gravity, however, is only noticeable on the macroscopic scale. Excluding gravity, these forces, along with the theory of the elementary particles, discussed in sec.(2.2), make the Standard Model of particle physics (SM). Quantum Field Theory (QFT), the framework that combines classical field theory, special relativity (SR) and quantum mechanics (QM) defines elementary particles as being excitations of fields, meaning that they are structureless objects. The elementary particles of the Standard Model are the Fermions and the Bosons.

2.1.1 Fermions

Fermions are categorized into leptons and quarks [9,10], both of which come in three generations, each being heavier than the previous, but all having spin-¹₂. The first generation is what all visible matter in the universe is made of and consists of the up- (u) and down- (d) quarks, the electron

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(e) and electron neutrino (νe) being the leptons. The second and third generation particles are unstable and quickly decay into the first generation. The generations are shown in Eqn.(2.1) where the first column (I) corresponds to the first generation and so on.

I II III

u d

! c

s

! t

b

!

e νe

! µ

νµ

! τ

ντ

!

(2.1)

Name Symbol Q [e] S C Be T B I L_e L_µ L_τ

down d −1/3 0 0 0 0 1/3 1/2 0 0 0

up u 2/3 0 0 0 0 1/3 1/2 0 0 0

strange s −1/3 −1 0 0 0 1/3 0 0 0 0

charm c 2/3 0 1 0 0 1/3 0 0 0 0

bottom b −1/3 0 0 −1 0 1/3 0 0 0 0

top t 2/3 0 0 0 1 1/3 0 0 0 0

electron e −1 0 0 0 0 0 0 1 0 0

e neutrino ν_e 0 0 0 0 0 0 0 1 0 0

muon µ −1 0 0 0 0 0 0 0 1 0

µ neutrino ν_µ 0 0 0 0 0 0 0 0 1 0

tauon τ −1 0 0 0 0 0 0 0 0 1

τ neutrino ντ 0 0 0 0 0 0 0 0 0 1

Table 1: Table of fermion quantum numbers. Q = charge (in units of the electron charge, e), S = strange, C = charm, eB = beauty, T = truth, B = baryon number, I = isospin, L = lepton number (three generations e, µ, τ ). Hypercharge Y = S + C + eB + T + B, third component of isospin I3≡ Q − Y /2. For antiparticles all signs of the quantum numbers are reversed, except for isospin.

The other generations of the leptons have the same quantum numbers. Taken from [11].

All particles have their own unique set of quantum numbers, for example the electric charge Q, baryon number B and lepton number L, as seen in Table 1. The proton is a bound state of the first generation quarks uud and the neutron is a bound state of udd. Taking the bound state of the proton for example, it is positively charged having a total charge 1 (Q = 1 = ²₃ +²₃ −¹₃) and a baryon number of 1 (B = 1 = ¹₃+¹₃ +¹₃), but no lepton number (L = 0). The fact that it has a baryon number of 1 makes it a baryon, a bound state of three quarks. The neutron, being a bound state of three quarks is also a baryon, but has a net charge of 0 which matches our previous knowledge of the characteristics of the neutron. The first generation of elementary particles also contain the electron and its corresponding neutrino, both of which have B = 0 and Le= 1, making them leptons. As previously mentioned, these four elementary particles make up all of the visible matter in the universe, since the combinations of u and d make protons and neutrons, which in turn make up the nuclei of all atoms, while the electron orbits it and the neutrino occasionally is emitted from the nuclei as a result of beta decay. Each particle, whether it be a quark or a lepton, has its own anti-particle. The anti-particle for the electron is the positron, with a positive electric charge in place of the negative and electron lepton number L_e= −1. The up-quark (u), for instance, has an anti-particle called the anti-up quark (u) or "u-bar" and is denoted by a bar over the symbol. Both the particle and its respective anti-particle have the same mass, but reversed signs for the quantum numbers (except for isospin). This leads to the possibility of a bound state of two quarks, called a meson. The meson consists of a quark and anti-quark pair with a baryon

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number of 0. As an example, the pion (π⁺) is composed of a bound state ud with baryon number B = 0 = ¹₃−¹₃ and naturally a lepton number of 0 (L = 0), confirming that it is neither a baryon nor a lepton, but a meson indeed. Different combinations of quarks from the first (I), second (II) and third (III) generations make up a plethora of baryons and mesons. These, however, decay very quickly, unlike the proton which has a mean lifetime of 10³¹years or the free neutron with a mean lifetime of just under 15 minutes [11]. The top (t) quark, being the heaviest of them all and having the shortest half-life, has not been observed in a bound state hadron.

Fermions also have a property called chiral handedness [12]. This quantum mechanical property differentiates particles form eachother. A particle can either have a left-handed or right-handed chirality. In order for a particle to interact with electroweak bosons through the weak interaction (see Sec.(2.1.2)), it needs to have a left-handed chirality, while its corresponding anti-particle needs to have a right-handed chirality. The remaining right-handed particle and the left-handed anti- particle are not affected by the weak interaction and therefore do not interact with the electroweak bosons.

2.1.2 Interactions and Force Carriers (Bosons)

Interactions between particles in the SM are mediated by what is known as the force carriers [10, 12]. An interaction could, for instance, be the decay of a particle into another through the emission of a force carrier or the collision of two particles which in turn create two new particles mediated through the force carrier. In total there are four force carriers corresponding to the three fundamental forces in the SM (gravity excluded), all under the banner of gauge bosons, having an spin = 1. The strong force is mediated by the gluon (g), the weak force by the W^± and Z⁰ bosons and the electromagnetic force by the photon (γ). The W^± boson has an electric charge of ±1, while the Z⁰boson, the gluon and the photon are electrically neutral, with the latter two also being massless. There are principles to how these gauge bosons can interact with the fermionic particles (and each other) and are described by the separate theories where they were first hypothesized.

The electromagnetic interaction is described by the theory of Quantum Electrodynamics (QCD) and has been unified with the weak interaction to create the Electroweak interaction. The strong interaction is described in the theory of Quantum Chromodynamics (QCD) but has also been unified together with the electroweak theory to describe today’s Standard Model.

2.2 Quantum Field Theory - The Language of the Infinitesimal

Classical mechanics studies the motion of bodies at a macroscopic scale - for instance, how an object moves when it is subject to a force or how a pendulum swings. Theories and rules applicable to such systems cease to work when either the object under study acquires a velocity close to the speed of light or if it has the size of an atom or subatomic particle. Albert Einstein’s Theory of Special relativity (SR) describes objects which travel close to or at the speed of light, whilst Quantum Mechanics (QM) handles objects of atomic sizes. In particle physics, the objects in question have both a relativistic velocity and quantum size, hence a theory unifying both of these requirements had to be constructed. The aforementioned theory is called the Quantum Field Theory (QFT) [12,13] and mathematically describes particles, not as tiny marbles as one would assume, but as excitations of fields. This treats the position (x) and momentum (p) variables as operators, such that

x → ˆx, p → ∂

∂x. (2.2)

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Similarly as in classical mechanics, the particles equation of motion (e.o.m) can be found from the Lagrange equation given by

d dt

∂L

∂ ˙q_i

− ∂L

∂q_i = 0 (2.3)

where the time-dependent, generalized coordinate of the particles is q_i = (x₁, x₂, x₃) and ˙q_i = dqi/dt. The solution to the Lagrange equation is the Lagrangian on the general form

L = T − V, (2.4)

where T and V are the kinetic and potential energy terms of the system. One can change the formalism from a discrete system into a continuous system with continuously varying coordinates φ(x, t) [9],

L(qi, ˙qi, t) → L

φ, ∂φ

∂xµ

, xµ

(2.5) such that one gets the Lagrangian when integrating the Lagrangian density over three dimensional space

L = Z

Ld³xi. (2.6)

The Action is defined as the space-time integral of the Lagrangian density

S = Z

path

Ld⁴x_µ (2.7)

and can derive the equation of motion of the particle by minimizing the action δS = 0, known as the principle of least action. Using this principle, one identifies the Euler-Lagrange equation

∂

∂xµ

∂L

∂(∂φ/∂xµ)

−∂L

∂φ = 0 (2.8)

with the four-vector xµ = (t, x1, x2, x3) which includes the time parameter. Since we are interested in expressing the Lagrangian in the formalism of fields, we will, following common practice, call L the Lagrangian itself.

The Lagrangians in QFT are a central part of particle physics, describing the properties of the particles and their interactions. In the following sections, they will be in focus when describing different theories and mechanisms.

Lagrangian functions are often subject to transformations in the coordinate system used to describe it. Noether’s theorem states that if the Lagrangian is not affected by the transformation, there will be a conservation of a quantity⁷. This links the conservation laws to another concept essential to particle physics - the abstract concept of symmetries. Symmetries can prelusively be thought of as the act of spinning a sphere around its axis - no matter how much it is turned in any axis, the sphere still looks the same. This means that the sphere has infinite symmetries, but a cube, for instance, has only 24. Simply put, a symmetry is a transformation which leaves the physical system unchanged. The interactions between particles follow certain symmetries in

7If the Lagrangian is independent of the angle of measurement, angular momentum is conserved, and so on.

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nature. Symmetries applicable to particle physics are called gauge symmetries and are continuous, local, internal symmetries. They are often represented as square matrices with different properties.

The simplest gauge symmetry is a 1 × 1 matrix⁸ called the Unitary matrix U(1) and is essentially a change in phase when applied to a Lagrangian. Another example of a symmetry is the Special Unitary matrix SU(N), with N × N unitary matrices with determinant 1 (det(U ) = 1) and the property of U^†U = U U^† = I, where I is the unit matrix. Symmetries relevant to the Standard Model will be described later in this section.

Transformations are operations which can be applied to Lagrangians. If a transformation leaves a Lagrangian unchanged or invariant it is said to be invariant under that transformation and the Lagrangian has a symmetry. A set of transformations forms a group [13]: the product of any two transformations is another transformation. This product is associative, has an identity transformation and an inverse. In particle physics, continuously symmetric groups are called Lie groups, which follow a Lie algebra [12].

The Standard model of particle physics has three combined groups - SU (3)_C× SU (2)L× U (1)Y, each corresponding to a conserved quantity. The SU (3)c group is a 3 × 3 matrix with the subscript c which stands for color charge. The group SU (2)_L× U (1)_Y is the group of the electroweak interaction, where the subscript L of the 2 × 2 group means that it only transforms the Left-handed states, leaving the Right-handed states unchanged. Y is short for the weak hypercharge quantum number.

Considering the U (1) gauge theory, it consists of a 1 × 1 matrix with a phase factor e^iα. Starting from the Dirac Lagrangian

L = ψ(x)(iγ^µ∂µ− m)ψ(x) (2.9)

where ψ is the Dirac spinor, m is the mass, µ is an index (going from 0 to 3) and γ^µis a conventional matrix called the gamma matrix which purpose is to ensure a correct matrix representation. A demand is set such that it is invariant under U (1) gauge transformation

φ(x) → φ⁰(x) = e^iαψ(x) ≡ U ψ(x). (2.10) If α = const. the Lagrangian is invariant under the transformation. But if α depends on x, i.e.α = α(x), the Lagrangian recieves an additional term when inserting (2.10) into (2.9)

L = e^−iα(x)ψ(x)(iγ^µ∂µ− m)e^iα(x)ψ(x)

= e^−iα(x)ψ(x)iγ^µ(i∂µα(x)e^iα(x)+ e^iα(x)∂µ)ψ − mψψ

= ψ(x)(iγ^µ∂µ− m)ψ(x) − ψiγ^µψi∂µα(x). (2.11) The last term is what prevents the Lagrangian from being invariant. To solve this problem a gauge covariant derivative is introduced which compensates the additional term

∂µ→ Dµ≡ ∂µ− igAµ, where Aµ→ Aµ+1

g∂µα(x) (2.12)

8A 1 × 1 matrix is just a scalar. For consistency, it is written as a matrix in the text.

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where g is the gauge coupling and Aµ is called the gauge field. Performing the same operation as in Eqn.(2.11), but using the covariant derivative from Eqn.(2.12) one finds

L = ψ(x)(iγ^µDµ− m)ψ(x) = ψ(x)(iγ^µ∂_µ− m)ψ(x) + gψγ^µψA_µ. (2.13) The Lagrangian turns out to be the original Dirac Lagrangian plus an additional term, dependent on the field A_µ which has to be introduced to make the Lagrangian invariant under the gauge transformation U (1). This additional term is a product of three fields with a gauge coupling g, called an interaction term. Setting the gauge coupling to the electric charge, −e and interpreting the field Aµ as the photon field, one finds that it is the gauge field of QED (its corresponding kinetic term is derived from the Maxwell equation).

As seen in the example above, covariant derivatives are of great importance since they hold the Lagrangian invariant under a gauge transformation at the "cost" of introducing additional fields. In Eqn.(2.12) the U (1) gauge group requires one vector boson to be invariant. The gauge groups SU (2) and SU (3), require three and eight vector bosons respectively. In SU (3), these are the linearly independent gluon color states G^k_µ, while in SU (2) there is one for each genera- tor W_µ^a = (W_µ¹, W_µ², W_µ³) which when combined together, give representations of the electrically charged vector bosons introduced in Sec.(2.1.2)

W_µ^± = 1

√2(−W_µ¹± iW_µ²). (2.14)

The electrically neutral weak bosons, Z⁰, is given by W_µ³ [12]. However, when it comes to derive the masses for the SU (2) gauge bosons, these are assumed massless, since the mass term in the Lagrangian Lmass = ¹₂m²W_µⁱW_j^µ for bosons, or Lmass,f = m ¯ψψ for fermions, is not invariant under gauge transformations. This is a problem since both bosons and fermions are massive, but fortunately, the solution to this problem lies in the Higgs mechanism.

2.3 Higgs boson and the Higgs Mechanism

As required by the gauge principle [12], the Standard Model must be locally gauge invariant under SU (3)_C× SU (2)_L× U (1)_Y, which requires that the fermions and gauge bosons remain massless for there to be gauge degrees of freedom. However, experiments show that the masses of the electroweak bosons (W^±, Z⁰) and fermions are well-defined, causing a discrepancy between theory and the observed experiments. The problem is solved by introducing a scalar field with a non-zero vacuum expectation value (vev), known as the Higgs field, as well as a mechanism for breaking the SU (3)_C× SU (2)_L× U (1)_Y symmetry down to SU (3)_C× U (1)_EM. This mechanism is called the Higgs Mechanism and comes with the prediction of a new elementary particle - the Higgs boson.

The spontaneous symmetry breaking from SU (3)C× SU (2)L× U (1)Y symmetry down to SU (3)C× U (1)EM constrains the choice of the minimal Higgs field. SU(2) requires it to take the form of a multiplet - minimally the doublet. The Higgs field is then written as a complex-doublet scalar field with four degrees of freedom

Φ = φ⁺(x) φ⁰(x)

!

= 1

√2

φ⁺₁(x) + iφ⁺₂(x) φ⁰₁(x) + iφ⁰₂(x)

!

(2.15)

where φ⁺₁(x), φ⁺₂(x), φ⁰₁(x) and φ⁰₂(x) are real, giving the four degrees of freedom in the Higgs field. By convention, the vacuum expectation value is assigned to the φ⁰₁(x) degree of freedom [12].

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Starting with the kinetic term of the Higgs field

T (Φ^†, Φ) = (DµΦ)^†(D^µΦ), (2.16) the Dµis the SU (3)C× SU (2)L× U (1)Y gauge-covariant derivative which contains the interactions of the fermions with the Higgs field. The Higgs potential is given by

V (Φ^†, Φ) = −µΦ^†Φ + λ(Φ^†Φ)², µ²> 0, λ > 0 (2.17) where λ is a coupling constant. It is worth to note that there are no odd powered terms in the potential, keeping the potential positive and allowing it a minimum non-zero value. For completeness, the kinetic and potential terms are inserted into Eqn.(2.4) to find the Lagrangian of the Higgs

LΦ= (DµΦ)^†(D^µΦ) + µΦ^†Φ − λ(Φ^†Φ)². (2.18) The vacuum expectation value is the minimum energy which can be found by deriving the Higgs potential in Eqn.(2.17) by Φ and setting it to zero.

dV (Φ)

dΦ = −2µ²Φ + 2λΦ³= 0 (2.19)

Ignoring degenerate and zero-point roots, the vacuum expectation value becomes

Φ = 1

√ 2

0 v

!

(2.20)

where Φ is the vacuum expectation value and v = pµ²/λ. This way, the physical vacuum is broken from a SU (3)C×SU (2)L×U (1)Y gauge-symmetry down to a SU (3)C×U (1)EM symmetry, with a non-zero Higgs vev [12]. Note here that the φ⁰₁(x) term from Eqn.(2.15) is the only component with a non-zero, charge-neutral value of v, effectively making the net charge of the scalar field 0. Concluding, both electromagnetism and the gluon field is not affected by the vev, thus leaving the SU (3)C× U (1)EM symmetries unbroken⁹.

The potential in Eqn.(2.17) is often called the Mexican hat potential due to its distinctive form, seen in Fig.(1). Radially, around the "tip of the hat" one finds a set of continuous non-zero minima, to which one parameterizes the Higgs field as

Φ(x) = e^iξ(x)·τ 1

√2 0 v + H(x)

!

, (2.21)

where ξ(x) are the excitations along the potential minimum, collectively called the Nambu-Goldstone Bosons (NGB) [12]. These NGBs are massless spin-0 particles, which, in the context of the Higgs mechanism, directly couple their degrees of freedom to the electroweak bosons. It is said that the bosons "eat up" the NGBs, effectively leaving them as massive spin-1 states, Z⁰ and W^±. The H(x) excitation corresponds to the massive free-particle state of the Higgs boson, which has a radial direction along the minimum of the potential.

9SU (3)C and U (1)EM are gauge groups corresponding to Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) respectively.

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Figure 1: Higgs potential as a three dimensional figure. At the local maximum, "tip of the hat", the symmetry is unbroken. The NGBs will arise at the minimum when the symmetry breaks.

The masses for the electroweak bosons are determined from the kinetic energy term of the Higgs Lagrangian, Eqn.(2.16) with the covariant derivative taking the form

Dµ= ∂µ− ig⁰Y

2Bµ− igτ_i

2W_µⁱ, (2.22)

where i can acquire the values i = 1, 2, 3 and Bµ is an electroweak boson field. The kinetic energy term becomes

(DµΦ)^†(D^µΦ) =(∂µ− ig⁰Y

2Bµ− igτi

2W_µⁱ)Φ†

(∂^µ− ig⁰Y

2B^µ− igτj

2W^µj)Φ (2.23) and using the previously derived Higgs vev from Eqn.(2.20) for the scalar field, the equation becomes

|DµΦ|²=1 8

g⁰Bµ+ gW_µ³ g(W_µ¹− iW_µ²) g(W_µ¹+ iW_µ²) g⁰B_µ+ gW_µ³

! 0 v

!

2

=v²g² 8

(W_µ¹)²+ (W_µ²)²

+v²

8

g⁰Bµ− gW_µ³

²

(2.24)

where both terms in the second equality of Eqn.(2.24) correspond to

1 2vg

²

W_µ⁺W^−µ, 1 2

1 2vp

g⁰²+ g²

²

ZµZ^µ (2.25)

respectively, when using the definitions of Eqn.(2.14), were Zµ=√ ¹

g⁰²+g²(gW_µ³−g⁰Bµ). Identifying the mass terms in the form of m²W⁺W⁻ and ¹₂m²Z⁰Z⁰, the masses become

MW =1

2vg, MZ =1 2vp

g⁰²+ g²= MW

pg⁰²+ g²

g = MW

cos(θW) (2.26) where g and g⁰ are the SU (2) and hypercharge couplings respectively and θW is the weak mixing angle or Weinberg angle, a free parameter determined by experiments [10].

Much like gauge bosons, fermions (quarks, leptons) are also massive particles but had theoretically no terms involving their mass in the SM. Similarly to the gauge bosons, the fermions get their mass through the Higgs mechanism. Briefly, consider the Yukawa interaction term with fermion fields, ψ, coupled to a complex scalar field φ

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LY ukawa= −cψφψ (2.27) where c is a real constant, referred to as the Yukawa coupling in the SM. Upon spontaneous symmetry breaking the Yukawa term takes the form of

LY ukawa= −cv

√

2ψψ − c

√

2H(x)ψψ (2.28)

where the first term relates to the mass of the fermion, with M_ψ = ^√¹

2cv and the second term is the coupling term between the fermions and the scalar field H(x), which is the Higgs excitation.

What constitutes the mass of the fermion is the coupling constant, c, and the vev, v. Eqn.(2.28) is a general equation where ψ is any fermion field (quarks or leptons), but since all fermions have different masses, the coupling constant c has to be different for every fermion. This also means that each fermion couples to the Higgs field with different strengths.

The gauge bosons and fermions needed a theory that would make them massive, which was only possible through the Higgs mechanism and would be proven correct when the Higgs Boson was discovered at the Large Hadron Collider (LHC) in 2012 by the ATLAS and CMS collaborations [1,2], ultimately completing the Standard Model.

2.4 The Hierarchy Problem

The ATLAS [1] and CMS [2] collaborations observed a particle consistent with the SM Higgs boson with mass

m_H = 125 ± 0.24 GeV [11] (2.29)

However, there seems to be a large discrepancy between the experimental mass and the theoretically predicted mass by the SM. Theoretically, the physical mass of the Higgs boson is divided into two parts - the loop corrections, which are divergent and the bare mass, defined as

m²_physical= m²_0−loop+X

n

m²_n−loop. (2.30)

At 0-loop level the mass corresponds to the non-divergent bare mass. The n-loop level corresponds to the divergent loop corrections which are of the order Λ²_SM GeV², assuming that the cut-off scale for the SM is of the order of the Plack scale, ΛSM ≤ 10¹⁹GeV. The reason for the cut-off scale is that the SM does not hold for energies above the Plack scale since the force of gravity becomes sufficiently large and would have to be accounted for. Calculating the mass of the Higgs boson theoretically would require the summation of all loop contributions with an expected mass proportional to Λ GeV. The measurement does, however, show a mass of ∼ 125 GeV, implying that the loop contribution terms may counteract each other through a very delicate fine-tuning between them. This is called the Hierarchy problem, addressing the fine-tuning problem and the concept of naturalness. The remaining part of the thesis will focus on the Hierarchy problem and a BSM scenario with a potential to solve it - the Composite Higgs model (CHM).

2.5 Composite Higgs Model

The Composite Higgs model (CHM) is an extension of the SM where the Higgs boson emerges as a pseudo Nambu-Goldstone boson (pNGB). The difference between NGB and pNGB is that

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the latter are massive¹⁰ and come from an approximate symmetry breaking. Apart from the SM sector, the CHM introduces a new strongly interacting composite sector with a global symmetry G = SO(5) (Special Orthogonal 5 × 5 matrix). This symmetry is spontaneously broken into H = SO(4) by breaking the Goldstone symmetry, resulting in the existance of NGBs. The number of NGBs is the number of broken generators, i.e. the difference in the number of generators between G and H, 10 − 6 = 4 (SO(N ) has N (N − 1)/2 generators). The four NGBs correspond to the four degrees of freedom of the Higgs doublet, present in the coset of G/H. The degrees of freedom are then used to trigger electroweak symmetry breaking (EWSB), by gauging the SO(4) subgroup GEW = SU (2)_L×U (1)Y with a covariant derivative. This corrects the Lagrangian, induc- ing an approximate symmetry and provides massive pNGBs when this symmetry is broken [14,15].

Consider the fiveplet ~Φ of real scalar fields with a Lagrangian from the strongly interacting composite sector [14]

L = 1

2∂µ~Φ^T∂^µΦ −~ g²_∗

8 (~Φ^TΦ − f )~ ². (2.31) where g_∗ is a coupling constant and f is the vev,Φ = f . In analogy to Eqn.(2.21), the field ~Φ can be parameterized as

Φ(x) = e~ ⁱ

√ 2 f Π_i(x) bTⁱ

"

0_4×1 f + σ(x)

#

, (2.32)

where Πi are the NGB fields and bTⁱ are the broken generators with i = 1,..,4. The σ(x) is the radial coordinate, similar to H(x) for the Higgs field in Eqn.(2.21), which in this case is a new resonance. The exponential term in Eqn.(2.32) is the Goldstone matrix U [Π], which can generally be applied to any symmetry breaking SO(N ) → SO(N − 1)¹¹

U [Π] = eⁱ

√2 f Π_i(x) bTⁱ

=

"

1 − (1 − cos(^Π_f))^Π~^~_Π^Π2^T sin(^Π_f))^Π_Π^~

− sin(^Π_f))^Π^~_Π^T cos(^Π_f)

#

, (2.33)

where Π =p ~Π^TΠ. Applying Eqn.(2.33) to Eqn.(2.32) yields~

Φ(x) =~

"

1 − (1 − cos ^Π_f)^~^Π~_Π^Π2^T sin ^Π_f~Π Π

− sin ^Π_fΠ~^T

Π cos ^Π_f

# "

04×1

f + σ(x)

#

= (f + σ(x))

"

sin ^Π_fΠ~ Π

cos ^Π_f

#

. (2.34)

Inserting the new field in Eqn.(2.34) into Eqn.(2.31) gives

L = 1

2∂µσ∂^µσ −(g_∗f )²

2 σ²−g²_∗f

2 σ³−g²_∗ 8 σ⁴ +1

2

1 +σ

f

2"

f²

Π²sin² Π f

∂_µΠ~^T∂^µΠ +~ f² 4Π⁴

Π²

f² − sin² Π f

∂_µ~Π²∂^µΠ~²

#

. (2.35)

The NGBs exist in the fourplet of SO(4), which can be written in terms of the Higgs doublet H = [hu, hd]

10I.e. not massless.

11A detailed derivation of the Goldstone matrix for SO(3) can be found in the Appendix of [16]

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Π =~





 Π₁ Π2

Π₃ Π4







= 1

√2







−i(h_u− h^†_u) hu+ h^†_u i(h_d− h^†_d)

hd+ h^†_d







(2.36)

The last step is to introduce the covariant derivative to the Lagrangian in Eqn.(2.31) in order to gauge SO(4) to its subgroup GEW = SU (2)L× U (1)Y

∂_µ→ Dµ= ∂_µ− igW_µ^αT_L^α− ig⁰B_µT_R³ (2.37) This yields the electroweak interactions of the theory. Breaking the SO(5) → SO(4) symmetry provides the degrees of freedom in the form of four NGBs in the minimal CHM. At the same time, the covariant derivative corrects the Lagrangian of Eqn.(2.31), giving it an approximate symmetry, which when explicitly broken through SO(5) → SO(4) yields pNGBs instead of NGBs. The Higgs doublet then arises as a pNGB as well as an exotic resonance in the form of a spin-1/2 Vector-like quark (VLQ). The VLQ under consideration is called the top-partner.

This subsection presented the minimal composite Higgs model (MCHM), which relies on the minimal number of pNGB fields and symmetry generators, serving as a illustrative example based on [14]. It does not solve the fine-tuning problem but gives an overview of how it may look like.

Briefly summarizing the theory considered in the model of the thesis, the CHM suggests that there exists two separate symmetry breakings in the theory. First, the large Ultracolor (UC) scale group, ΛU C, which considers a regime of free ultrafermions¹² [17], is broken into a group with condensates (i.e. bound states of ultrafermions), including the Higgs doublet which arises as a pNGB from a parallel symmetry breaking. The symmetry is then broken again, but at weak scale at 250 GeV, where the Higgs doublet acquires a vev and breaks the EW group SU (2)L× U (1)Y, in contrast to the Higgs mechanism.

2.6 Exotic Decays of top Partners

The model on which this thesis is based on, comes from the work of [18]. It considers a more complex theory than the MCHM, predicting a pNGB Higgs as well as an exotic resonance in the form of a spin-1/2 Vector-like quark (VLQ). The VLQ under consideration is called the top-partner, denoted with a capital T. Additionally, the model predicts an neutral composite scalar, S¹³, which couples to the top-partner.

The heavy top-partner is assumed to pair produce¹⁴ and decay to the SM gauge bosons and third generation quarks, seen in Eqn.(2.38). The decay channels are

T → W b, T → Ht, T → Zt (2.38)

where W and Z are the SM gauge bosons, H is the Higgs boson and t is the SM top quark.

However, the top-partner is also expected to decay via the neutral composite scalar, S and the top quark

12BSM fermions, analogous to SM fermions.

13The symbol for the S particle is in some papers denoted as η.

14Pair-production of top-partners is just one possibility, but it is model-independent.

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Figure 2: Branching ratio of S as a function of mS. Figure from [4].

T → St, (2.39)

which is the main focus of the thesis.

The Lagrangian, on which the model is based on is the SM Lagrangian with the addition of coupling terms related to the resonances T and S. Consider the following Lagrangian for the top-partner

LT = T (iD − M_T)T − (iK_T_LT SP_Lt + L ↔ R + h.c.). (2.40) Since this thesis only investigates the interaction involving T and S, only the relevant term is written out. Here KTL is the coupling term for the left-handed top-partner (TL), which is at its extreme when KT_R = 0. PL is a left-handed projector defined as P_L/R = (1 ± γ⁵)/2. In the same manner, the Lagrangian for the scalar with couplings to the SM gauge bosons is written as

LS =1

2(∂µS)(∂^µS) −1

2m²_SS²+ g_s²K_g^S 16π²fS

SGâ_µνGeâµν+g²K_Wâ 8π²fS

SW_µν⁺Wf^−µν+ e²K_γ^S 16π²fS

SAµνAe^µν

+g²c²_WK_Z^S 16π²fS

SZ_µνZe^µν+egc_WK_Zγ^S 8π²fS

SA_µνZe^µν. (2.41)

In Eqn.(2.41) the first and second term is the kinetic and mass term of S, respectively. The rest are coupling terms allowing S to decay into the electroweak bosons W^±, Z, the photon (A) and the gluon (G), with coupling constants K_W^a (a = 1, . . . , 8), c²_WK_Z^S, cWK_Zγ^S , K_γ^S and K_g^S. fS is the decay constant and the tilde (∼) above the symbols signify a dual field strength tensor, Xe_µν =¹₂_µναβX^αβ, where X can be G, W , A or Z and is the Levi-Civita tensor. From Eqn.(2.41), the following di-boson channels are possible

S → gg, S → W⁺W⁻, S → γγ, S → Z⁰Z⁰, S → Z⁰γ. (2.42)

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Coupling terms with fermions are left out for simplicity. Because S arises as a singlet from a group that embeds the EW sector, the coefficient K_g^S is set to zero, leaving only coupling terms to EW bosons. For simplicity, K_γ^S = 0, such that S does not decay through a di-photon channel. It is very much possible to have non-zero BR to γγ orf f , where f are fermions. However, when rewriting the Lagrangian in Eqn.(2.41) into Eqn.(A.1) the coupling to photons vanishes [4].

Fig.(2) shows the branching ratio (BR) of S as a function of mS. For low masses of S the decay rates are model dependent [4], only decaying into Z⁰γ, therefore the focus will be put on the mS > 2m_Z range (∼ 180 GeV), where the branching ratios are considered constant.

The Feynman diagram representing the decay of the pair-produced top-partners to the neutral scalar S is shown in Fig.(3). From here, it is assumed that the t quark decays into a b quark and a W^± boson as observed in the SM, while the S particle can decay through any channel shown in Fig.(4), which shows all possible decay channels of S and their corresponding branching ratios, excluding the S → γγ channel.

g T

T¯

¯ u u

t¯ S S t

Figure 3: T ¯T production and decay to a new scalar S.

S

ZZ

llll 0.01

llνν 0.04

νννν 0.04

jjjj 0.49

jjνν 0.28

lljj 0.14

0.16

Zγ

jjγ 0.70

llγ

0.10

ννγ 0.20 0.19

W⁺W⁻

lνlν 0.10

lνjj

0.44

jjjj 0.46 0.65

Figure 4: Branching ratio tree of all final decay products of neutral scalar S. Each final state corresponds to a branching ratio. ν = neutrino (any flavour), l = lepton (any flavour), γ = photon and j = quark jet (any flavour). Approximated from [11].

2.7 Summary of ATLAS Searches for Vector-like Quarks

Previous searches for a vector-like top-partner have only considered it decaying into standard model particles, with fermions of the 3rd generation. They have mainly assumed a pair production

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of the top-partner and a case where the top-partner is singly produced in the decay channels T T → Ht + X [19], T T → Zt + X [20], T T → W b + X [21] and Y → Ht [22], where X is some decay product. Although there is no evidence for VLQ production at the LHC, lower limits of the top-partner mass at 95% confidence level (CL) have been observed to be between 0.99 and 1.43 TeV [23]. This limit is however not strictly the same for the decay channel considered in this thesis, since it may vary from model to model. For this reason, the scan of the top-partner mass will be set to start from 800 GeV - slightly below the limit found by the previous searches.

3 Simulation

Modern particle physics methods of analyzing Beyond the Standard Model (BSM) physics rely heavily on experimental data and simulations based on the framework and theory of the underlying model. A brief description of the detectors layout is presented, as well as what information about the particles can be extracted from it, followed by the tools that were used to generate appropriate signals.

3.1 ATLAS Detector

The ATLAS general purpose detector is a part of the LHC accelerator complex, which also houses the CMS, ALICE and LHCb detectors. It is constructed in a cylindrical manner¹⁵, in which the different particle detectors encompass the beam axis which passes through the center of the detector. Closest to the beam axis is the inner tracking device which reveal the path of electrically charged particles, like the electron. Around the tracking device there is an electromagnetic calorimeter which detects electromagnetic particles such as the electron and photon by measuring their energy loss as they pass through it. The calorimeter can not differentiate between these two particles, but since the electron is a charged particle and the photon is not, the information from the inner tracking device can be used to distinguish the particles. Enclosing the electromagnetic calorimeter is the hadronic calorimeter and works similarly, by measuring the energy loss from hadronic particles, such particles containing quarks (mesons, baryons) or hadronic showers¹⁶. On the outer rim of the detector there is a muon spectrometer, which detects muons. It is placed farthest away because muons interact very little with matter and pass through the inner detector and calorimeters. Neutrinos only interact weakly with matter and therefore have a very low interaction probability. They are therefore not detected in the traditional meaning, but instead are indirectly detected through the fact that their transverse momentum is not measured and thus the net transverse energy in the detector is non-zero as explained below.

From detection, only certain parameters can be derived. When a particle is absorbed by the calorimeter, its energy and angle is recorded. The total angle is subdivided into two parameters, η(θ) and φ. η is the pseudorapidity and is commonly used to describe the angle between the position of the particle and transverse plane (beam axis, passing through the center of the cylindrical detector) in the center of the detector. When η = 0, the particle is purely in the transverse plane (i.e. θ = 90^◦from the beam axis) but when η → ∞, the particle is parallel (i.e. θ = 0^◦) to the beam axis¹⁷ since η ≡ −lntan(θ/2). φ is the azimuthal angle and together with the pseudorapidity, η, the exact position of the particle detection is calculated. As mentioned, neutrinos can not be

1525m in diameter and 44m in length

16Hadronic showers arise from the phenomenon of color confinement, where quarks clump together to form mesons or baryons, resulting in a cascade of secondary particles created from the vacuum of space.

17It can not be detected since no detectors can be placed in the path of the beam.

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detected in any calorimeter, however they have momentum like any other particle. Before the collision, the only momentum in the system is along the axis of the beam, which means that there is no transverse momentum, so when measuring the net transverse momentum of all particles after the collision, one would expect a nil net transverse momentum. Because of the undetected neutrinos, there will be a certain transverse momentum missing from the system, which would have made the net transverse momentum of the system equal to zero. This transverse momentum relates to the neutrinos and is called missing transverse momentum¹⁸, denoted by P_T^miss. Computer algorithms take the information from the detector and attempt to reconstruct the vertices from the position and energy of the detected particles. Using a fast detector simulator¹⁹, Delphes [7], a model of the ATLAS detector will be used to simulate signal events for BSM interactions and particles in this thesis.

3.2 Signal Generation - MadGraph 5

MadGraph 5 is an open source software written in Python for the generation of matrix elements at the tree-level for any model [5]. Tree-level diagrams are Feynman diagrams without loops representing the "pure" signal of the desired model. Here, the Feynman diagram starts with the collision of two protons, i.e.two quarks, two gluons or one of each, followed by the chain of relevant particles and interactions of interest. However, the colliding particles depend on which accelerator one desires to mimic²⁰. The diagram can either be modeled from start to finish, specifying each particle in the decay chain or specifying only the colliding particles and the particles of most interest, leaving the software to fill in all the possible topologies in between.

Simulations like these are often used in BSM theories and can be generated if a detailed input model file is provided. Model files contain all of the SM + BSM couplings between particles as well as their respective decays, propagators and vertices. It is in this file that theoretical parameters of new particles are inserted in order to describe how they interact and behave. Apart from the model file, parameters like the total center-of-mass energy,√

s and number of events is selected, among other.

MadGraph 5 outputs Les Houches Event Files (lhe) [24] written in the most basic format with events separated from each other. Each event in the lhe file contains all of the necessary information per particle in order to derive its energy, momentum, pseudorapidity, daughter particle among other. Because the output contains events at parton-level (events at the most basic level, i.e.Feynman diagrams), it serves as a good tool to investigate the kinematics of an event. However, the amount of information about the events and the fact that there exist "free" quarks is not realistic, meaning that additional tools are required to make each event feasible.

3.3 Signal Hadronization and Detector Simulation - Pythia8 & Delphes

In order to make the signal more realistic, the event file (lhe file) has to be put through hadroni- sation and parton showers, followed by a fast detector simulation.

Pythia8 [6] is a software that hadronises and showers each signal event generated by MadGraph 5,

18Very often, missing transverse energy (E_T^miss) is used instead, where it is given a direction by the azimuthal angle φ. These terms are analogous in relation to neutrinos, with the momentum being a vector instead of a scalar as in the case of energy.

19See Sec.(3.3)

20Proton-(anti)proton or proton-electron collider, etc.

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using Monte Carlo methods that simulate fluctuations in the final states. For every fermion in the final state of the signal, Pythia8 either showers it electromagnetically if it is a lepton (excluding the muon) or photon, or generates a hadron shower (quark-jet) for every "free" quark in the signal event. The purpose is to make each event as realistic as possible²¹, which means that generating additional fluctuations in the events is necessary. The output of the program is a .hepmc file containing all particles present in each event. These contain among other parameters, the momentum, energy and pseudorapidity of the particles.

The showered and hadronised events are at this point an approximation of reality. However, certain constraints exist when particles are to be detected. Limitations in the detectors ability to reconstruct signal events make it necessary for a fast detector simulation to take place. Delphes [7], a fast detector simulator, reads the showered signal event files and filters which events or particles are detected. The constraints range from where the detectors are, their blindspots/gaps between the detectors, the probability to reconstruct the signal correctly and many more. An important constraint is also the detectors incapability of detecting neutrinos, since they interact weakly with matter. This means that there will be an imbalance in energy and momentum of the system, making it difficult to correctly identify the signal. Therefore missing transverse momentum (P_T^miss) and energy (E_T^miss) will be parameters taken into account in regards to neutrinos. The choice of detector plays a role on how the signal events are reconstructed, two of the most common ones being the ATLAS and CMS detectors. In this thesis, the ATLAS detector will be in focus, since it is a high-energy general purpose detector and has its models and recasts already implemented in the software.

4 Recast

Recasting is a technique that uses existing searches for new physics to constrain alternative models of interest [25, 8]. Analyses of models are performed by experimentalists, who design a particular signal and look for its final state particles in data measured by the detector, by applying cuts to it. By cutting away events that do not resemble the signal of interest, one can minimize the SM background in relation to the sought-after signal. Cuts are sets of selection criteria which one applies to events reconstructed in the detector, ranging from the number of jets a signal should have to what the missing energy of that signal should be. As an example, consider a search for a signal that has at least 3 jets, a certain missing transverse energy no less than 250 GeV and photons, but strictly no leptons. One then applies appropriate cuts or selection criteria to the set of data: If the event contains less than 3 jets, a missing transverse energy of 150 GeV or one lepton - the event is discarded, i.e.the final state particles do not resemble the signal one is looking for. After applying the cuts, some of the data may be filtered out, leaving candidate events which pass the cuts of a signal region (SR). Signal regions are regions in the parameters space where a signal would be expected and where the background is minimized through the application of cuts. The number of signal regions depends on how the search was conducted, but conclusively, only the signal region which is most sensitive to the signal is of importance. An analysis of the signal regions (SR) is then done to see if the candidate events are of any interest. After the analysis is completed, and no significant excess of signal to background is found, its results can be used further, by projecting an alternative model onto it. The alternative model, with a different signal, will then have the same cuts applied to it as the existing analysis. This is called recasting and allows the application of the

21In comparison to what has been measured in the detector.

Exotic Decays of a Vector-like top Partner at the LHC

Examensarbete 30 hp September 2019

Exotic Decays of a Vector-like top Partner at the LHC

Alexander Skwarcan-Bidakowski

Abstract

Exotic Decays of a Vector-liketop Partner at the LHC

Alexander Skwarcan-Bidakowski

Contents

Populärvetenskaplig sammanfattning

1 Introduction

2 Theory

2.1 Standard Model of Particle Physics

2.2 Quantum Field Theory - The Language of the Infinitesimal

2.3 Higgs boson and the Higgs Mechanism

2.4 The Hierarchy Problem

2.5 Composite Higgs Model

2.6 Exotic Decays of top Partners

2.7 Summary of ATLAS Searches for Vector-like Quarks

3 Simulation

3.1 ATLAS Detector

3.2 Signal Generation - MadGraph 5

3.3 Signal Hadronization and Detector Simulation - Pythia8 & Delphes

4 Recast